Your methodology was all good. But did you lock the carriage to the bed, and preferably lock the topslide too for best results?

But parting is not a precision operation. Within 0.1mm is not too bad. Often the parting tool will not go in dead straight if it is not set dead on square to the lathe axis or if the end of the parting tool is not ground dead square.

Best to part off a bit oversize and then face off the end to final size. You get a better finish that way too.

Either that or make up a washer chuck to hold it. A piece of round stock with a recess to fit the thin slice you have, then slit so it can be squeezed down slightly in the three jaw chuck. Easier to mount iton the crank and take a light skim I reckon.

Next time use a black marker to paint the OD and put a line on it near your desired cut length. I use a cheap digital caliper, set the distance and just use the hardened tip to scribe the line. Now bring your parting blade just left of the line, wind back the compound (set parallel to the bed) a little to make sure there's no backlash and take a shallow parting cut. Measure the piece from the end to the cut with a caliper and then retract the tool and wind back the compound to suit your finished size. Your piece should be very close to length when you part it now.